Lectures on Formal and Rigid Geometry

• Classical Rigid Geometry.- Tate Algebras.- Affinoid Algebras and their Associated Spaces.- Affinoid Functions.- Towards the Notion of Rigid Spaces.- Coherent Sheaves on Rigid Spaces.- Formal Geometry.- Adic Rings and their Associated Formal Schemes.- Raynaud's View on Rigid Spaces.- More Advanced Stuff.- Appendix.- References.- Index.

“Its aim is to offer a rapid and mostly self-contained ‘lecture-style’ introduction to the theory of classical rigid geometry established by Tate, together with the formal algebraic geometry approach set up by Raynaud. Furthermore, the volume provides enlightening examples of rigid spaces and points out analogies with and differences from the theory of schemes. The book is suitable for a first course on formal and rigid geometry, but it can be used equally well for personal study.” (Alessandra Bertapelle, Mathematical Reviews, March, 2016)“All notions introduced are discussed thoroughly, proofs are lucid and elegant, and the hypotheses made and their relevance are clear throughout the text. … The reader comes away from the text with a thorough understanding of the internal motivations of the theory of formal and rigid spaces. The bookis an extremely readable introduction to its subject, as well as to the techniques of modern geometry in general.” (Jeroen Sijsling, zbMATH 1314.14002, 2015)